Question

The $H$ amount of thermal energy is developed by a resistor in $10 s$ when a current of $4 A$ is passed through it If the current is increased to $16 A$, the themal energy developed by the resistor in $10 s$ will be:

• A. $\frac{ H }{4}$
• B. H
• C. $4 H$
• D. $16 H$

Hint:

The thermal energy developed in a resistor is proportional to the square of the current.

Answer 1

The Correct Option is D

To solve this question, we need to use the formula for thermal energy developed in a resistor, which is given by Joule's law of heating:

\(H = I^2 R t\)

Where:

• \(H\) is the thermal energy developed,
• \(I\) is the current passing through the resistor,
• \(R\) is the resistance of the resistor,
• \(t\) is the time for which the current flows.

According to the question, when a current of 4 A is passed through the resistor for 10 seconds, the thermal energy developed is \(H\). We can write this as:

\(H = (4)^2 R \times 10 = 16 \times R \times 10\) (Equation 1)

Now, we need to find the thermal energy when the current is increased to 16 A for the same time period of 10 seconds. Using the formula again, we write:

\(H' = (16)^2 R \times 10 = 256 \times R \times 10\)

To find the relationship between the new thermal energy \(H'\) and the initial thermal energy \(H\), we compare Equation 1 with this result:

\(\frac{H'}{H} = \frac{256 \times R \times 10}{16 \times R \times 10} = \frac{256}{16} = 16\)

So, \(H' = 16H\)

Therefore, the thermal energy developed by the resistor when the current is increased to 16 A for 10 seconds will be \(16H\).

The correct answer is: \(16H\).